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arXiv · 1810.05103

Linear $\ell$-Intersection Pairs of Codes and Their Applications

Kenza Guenda·T. Aaron Gulliver·Somphong Jitman·Satanan Thipworawimon
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Abstract

In this paper, a linear $\ell$-intersection pair of codes is introduced as a generalization of linear complementary pairs of codes. Two linear codes are said to be a linear $\ell$-intersection pair if their intersection has dimension $\ell$. Characterizations and constructions of such pairs of codes are given in terms of the corresponding generator and parity-check matrices. Linear $\ell$-intersection pairs of MDS codes over $\mathbb{F}_q$ of length up to $q+1$ are given for all possible parameters. As an application, linear $\ell$-intersection pairs of codes are used to construct entanglement-assisted quantum error correcting codes. This provides a large number of new MDS entanglement-assisted quantum error correcting codes.

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Kenza Guenda, T. Aaron Gulliver, Somphong Jitman, Satanan Thipworawimon. 2018-10-11. Linear $\ell$-Intersection Pairs of Codes and Their Applications. https://arxiv.org/abs/1810.05103

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